Notwithstanding the undeniable success of telecoms liberalisation in terms of price reduction, new services and technologies as well as consumer satisfaction, EU telecoms policy is at least a half failure. This might seem hard to believe, but we show in this paper that there is no such thing as an EU telecoms (or eComms) single market. We provide ample empirical economic and regulatory evidence of profound and lingering fragmentation as well as a brief assessment of the flaws of the eComms package as amended in 2009, and recently entered into force. Overcoming the fragmentation cannot but yield a considerable welfare improvement for the Union, which is exactly what a single market should be expected to deliver. Doing away with the flaws in the EU system requires a better institutional design. We wonder whether the regulatory (and competition policy) approach is really suitable for the Union and whether the fundamental conflict between the EU constitutional doctrine and the building of the single market (just as much a constitutional duty!) should not be resolved in novel ways.